% Mizar problem: t23_heyting2,heyting2,1093,56 
fof(t23_heyting2,conjecture,(
    ! [A,B] : 
      ( v1_finset_1(B)
     => ! [C] : 
          ( m2_subset_1(C,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B))
         => k2_lattice2(k4_partfun1(A,B),k5_substlat(A,B),C,k8_heyting2(A,B)) = k10_setwiseo(k4_partfun1(A,B),k4_partfun1(A,B),C,k11_setwiseo(k4_partfun1(A,B))) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v3_lattices,antisymmetry_r2_hidden,cc1_finseq_1,cc1_finsub_1,cc1_fraenkel,cc1_funct_1,cc1_relset_1,cc1_substlat,cc2_finsub_1,cc2_funct_1,cc2_substlat,cc3_finsub_1,commutativity_k1_finsub_1,commutativity_k2_substlat,commutativity_k2_xboole_0,commutativity_k5_setwiseo,d10_xboole_0,d1_funct_2,d1_substlat,d3_lattice2,d3_tarski,d4_substlat,d5_finsub_1,dt_g3_lattices,dt_k10_setwiseo,dt_k11_setwiseo,dt_k1_binop_1,dt_k1_finsub_1,dt_k1_funct_1,dt_k1_partfun1,dt_k1_relat_1,dt_k1_setwiseo,dt_k1_substlat,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_binop_1,dt_k2_lattice2,dt_k2_partfun1,dt_k2_relat_1,dt_k2_setwiseo,dt_k2_substlat,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_binop_1,dt_k3_substlat,dt_k4_partfun1,dt_k4_relset_1,dt_k4_substlat,dt_k5_finsub_1,dt_k5_lattices,dt_k5_relat_1,dt_k5_relset_1,dt_k5_setwiseo,dt_k5_substlat,dt_k7_funct_2,dt_k7_relat_1,dt_k7_setwiseo,dt_k8_funct_2,dt_k8_heyting2,dt_l1_lattices,dt_l1_struct_0,dt_l2_lattices,dt_l3_lattices,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_lattices,dt_u1_struct_0,dt_u2_lattices,existence_l1_lattices,existence_l1_struct_0,existence_l2_lattices,existence_l3_lattices,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc11_finseq_1,fc17_finseq_1,fc1_finsub_1,fc1_funct_1,fc1_rfinseq,fc1_struct_0,fc1_subset_1,fc1_substlat,fc1_wellfnd1,fc2_finseq_1,fc2_finsub_1,fc2_subset_1,fc2_substlat,fc3_substlat,fc4_funct_1,fc4_subset_1,fc4_substlat,fraenkel_a_2_0_substlat,fraenkel_a_2_1_heyting2,free_g3_lattices,idempotence_k1_finsub_1,idempotence_k2_substlat,idempotence_k2_xboole_0,idempotence_k5_setwiseo,l37_heyting2,rc1_finseq_1,rc1_fraenkel,rc1_funct_1,rc1_heyting2,rc1_setwiseo,rc1_subset_1,rc1_substlat,rc2_funct_1,rc2_setwiseo,rc2_subset_1,rc2_substlat,rc3_finseq_1,rc3_funct_1,rc3_struct_0,rc4_funct_1,rc5_struct_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k1_finsub_1,redefinition_k1_partfun1,redefinition_k2_binop_1,redefinition_k2_partfun1,redefinition_k2_setwiseo,redefinition_k2_substlat,redefinition_k4_relset_1,redefinition_k5_relset_1,redefinition_k5_setwiseo,redefinition_k7_funct_2,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r1_heyting1,reflexivity_r1_heyting1,reflexivity_r1_tarski,s4_funct_2__e5_37__heyting2,t11_substlat,t13_substlat,t14_setwiseo,t19_funct_2,t1_boole,t1_subset,t21_funct_2,t26_lattice2,t26_substlat,t27_lattice2,t28_lattice2,t29_lattice2,t2_heyting2,t2_subset,t2_tarski,t3_subset,t46_relat_1,t4_subset,t5_subset,t65_setwiseo,t67_lattice2,t67_setwiseo,t68_setwiseo,t69_lattice2,t6_boole,t6_heyting2,t70_setwiseo,t72_funct_1,t7_boole,t7_substlat,t8_boole,t8_substlat,t91_relat_1,t9_funct_1,t9_substlat]),
    [file(heyting2,t23_heyting2)]).

fof(abstractness_v3_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( v3_lattices(A)
       => A = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ) ) ),
    file(lattices,v3_lattices),
    []).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc1_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_1),
    []).

fof(cc1_finsub_1,axiom,(
    ! [A] : 
      ( v4_finsub_1(A)
     => ( v1_finsub_1(A)
        & v3_finsub_1(A) ) ) ),
    file(finsub_1,cc1_finsub_1),
    []).

fof(cc1_fraenkel,axiom,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(fraenkel,cc1_fraenkel),
    []).

fof(cc1_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(cc1_substlat,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_substlat(A,B))
     => v1_finset_1(C) ) ),
    file(substlat,cc1_substlat),
    []).

fof(cc2_finsub_1,axiom,(
    ! [A] : 
      ( ( v1_finsub_1(A)
        & v3_finsub_1(A) )
     => v4_finsub_1(A) ) ),
    file(finsub_1,cc2_finsub_1),
    []).

fof(cc2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    []).

fof(cc2_substlat,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_substlat(A,B))
     => ( v1_finset_1(C)
        & v1_fraenkel(C) ) ) ),
    file(substlat,cc2_substlat),
    []).

fof(cc3_finsub_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k5_finsub_1(A))
     => v1_finset_1(B) ) ),
    file(finsub_1,cc3_finsub_1),
    []).

fof(commutativity_k1_finsub_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k1_finsub_1(A,B,C) = k1_finsub_1(A,C,B) ) ),
    file(finsub_1,k1_finsub_1),
    []).

fof(commutativity_k2_substlat,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(C,k1_substlat(A,B))
        & m1_subset_1(D,k1_substlat(A,B)) )
     => k2_substlat(A,B,C,D) = k2_substlat(A,B,D,C) ) ),
    file(substlat,k2_substlat),
    []).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(commutativity_k5_setwiseo,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k5_finsub_1(A))
        & m1_subset_1(C,k5_finsub_1(A)) )
     => k5_setwiseo(A,B,C) = k5_setwiseo(A,C,B) ) ),
    file(setwiseo,k5_setwiseo),
    []).

fof(d10_xboole_0,axiom,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    []).

fof(d1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    []).

fof(d1_substlat,axiom,(
    ! [A,B] : k1_substlat(A,B) = a_2_0_substlat(A,B) ),
    file(substlat,d1_substlat),
    []).

fof(d3_lattice2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & l3_lattices(B) )
         => ! [C] : 
              ( m1_subset_1(C,k5_finsub_1(A))
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,u1_struct_0(B))
                    & m2_relset_1(D,A,u1_struct_0(B)) )
                 => k2_lattice2(A,B,C,D) = k7_setwiseo(A,u1_struct_0(B),u2_lattices(B),C,D) ) ) ) ) ),
    file(lattice2,d3_lattice2),
    []).

fof(d3_tarski,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    []).

fof(d4_substlat,axiom,(
    ! [A,B,C] : 
      ( ( v3_lattices(C)
        & l3_lattices(C) )
     => ( C = k5_substlat(A,B)
      <=> ( u1_struct_0(C) = k1_substlat(A,B)
          & ! [D] : 
              ( m2_subset_1(D,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B))
             => ! [E] : 
                  ( m2_subset_1(E,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B))
                 => ( k1_binop_1(u2_lattices(C),D,E) = k3_substlat(A,B,k2_substlat(A,B,D,E))
                    & k1_binop_1(u1_lattices(C),D,E) = k3_substlat(A,B,k4_substlat(A,B,D,E)) ) ) ) ) ) ) ),
    file(substlat,d4_substlat),
    []).

fof(d5_finsub_1,axiom,(
    ! [A,B] : 
      ( v4_finsub_1(B)
     => ( B = k5_finsub_1(A)
      <=> ! [C] : 
            ( r2_hidden(C,B)
          <=> ( r1_tarski(C,A)
              & v1_finset_1(C) ) ) ) ) ),
    file(finsub_1,d5_finsub_1),
    []).

fof(dt_g3_lattices,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A) )
     => ( v3_lattices(g3_lattices(A,B,C))
        & l3_lattices(g3_lattices(A,B,C)) ) ) ),
    file(lattices,g3_lattices),
    []).

fof(dt_k10_setwiseo,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(C,k5_finsub_1(A))
        & v1_funct_1(D)
        & v1_funct_2(D,A,k5_finsub_1(B))
        & m1_relset_1(D,A,k5_finsub_1(B)) )
     => m1_subset_1(k10_setwiseo(A,B,C,D),k5_finsub_1(B)) ) ),
    file(setwiseo,k10_setwiseo),
    []).

fof(dt_k11_setwiseo,axiom,(
    ! [A] : 
      ( v1_funct_1(k11_setwiseo(A))
      & v1_funct_2(k11_setwiseo(A),A,k5_finsub_1(A))
      & m2_relset_1(k11_setwiseo(A),A,k5_finsub_1(A)) ) ),
    file(setwiseo,k11_setwiseo),
    []).

fof(dt_k1_binop_1,axiom,(
    $true ),
    file(binop_1,k1_binop_1),
    []).

fof(dt_k1_finsub_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => m1_subset_1(k1_finsub_1(A,B,C),A) ) ),
    file(finsub_1,k1_finsub_1),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

fof(dt_k1_partfun1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( v1_funct_1(E)
        & m1_relset_1(E,A,B)
        & v1_funct_1(F)
        & m1_relset_1(F,C,D) )
     => ( v1_funct_1(k1_partfun1(A,B,C,D,E,F))
        & m2_relset_1(k1_partfun1(A,B,C,D,E,F),A,D) ) ) ),
    file(partfun1,k1_partfun1),
    []).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

fof(dt_k1_setwiseo,axiom,(
    ! [A] : 
      ( v1_xboole_0(k1_setwiseo(A))
      & m1_subset_1(k1_setwiseo(A),k5_finsub_1(A)) ) ),
    file(setwiseo,k1_setwiseo),
    []).

fof(dt_k1_substlat,axiom,(
    ! [A,B] : m1_subset_1(k1_substlat(A,B),k1_zfmisc_1(k5_finsub_1(k4_partfun1(A,B)))) ),
    file(substlat,k1_substlat),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_binop_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_subset_1(E,A)
        & m1_subset_1(F,B) )
     => m1_subset_1(k2_binop_1(A,B,C,D,E,F),C) ) ),
    file(binop_1,k2_binop_1),
    []).

fof(dt_k2_lattice2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B)
        & m1_subset_1(C,k5_finsub_1(A))
        & v1_funct_1(D)
        & v1_funct_2(D,A,u1_struct_0(B))
        & m1_relset_1(D,A,u1_struct_0(B)) )
     => m1_subset_1(k2_lattice2(A,B,C,D),u1_struct_0(B)) ) ),
    file(lattice2,k2_lattice2),
    []).

fof(dt_k2_partfun1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => ( v1_funct_1(k2_partfun1(A,B,C,D))
        & m2_relset_1(k2_partfun1(A,B,C,D),A,B) ) ) ),
    file(partfun1,k2_partfun1),
    []).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    []).

fof(dt_k2_setwiseo,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m1_subset_1(k2_setwiseo(A,B),k5_finsub_1(A)) ) ),
    file(setwiseo,k2_setwiseo),
    []).

fof(dt_k2_substlat,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(C,k1_substlat(A,B))
        & m1_subset_1(D,k1_substlat(A,B)) )
     => m1_subset_1(k2_substlat(A,B,C,D),k5_finsub_1(k4_partfun1(A,B))) ) ),
    file(substlat,k2_substlat),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k3_binop_1,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A) )
     => m1_subset_1(k3_binop_1(A,B),A) ) ),
    file(binop_1,k3_binop_1),
    []).

fof(dt_k3_substlat,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B)))
     => m2_subset_1(k3_substlat(A,B,C),k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B)) ) ),
    file(substlat,k3_substlat),
    []).

fof(dt_k4_partfun1,axiom,(
    $true ),
    file(partfun1,k4_partfun1),
    []).

fof(dt_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(relset_1,k4_relset_1),
    []).

fof(dt_k4_substlat,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B)))
        & m1_subset_1(D,k5_finsub_1(k4_partfun1(A,B))) )
     => m1_subset_1(k4_substlat(A,B,C,D),k5_finsub_1(k4_partfun1(A,B))) ) ),
    file(substlat,k4_substlat),
    []).

fof(dt_k5_finsub_1,axiom,(
    ! [A] : v4_finsub_1(k5_finsub_1(A)) ),
    file(finsub_1,k5_finsub_1),
    []).

fof(dt_k5_lattices,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_lattices(A) )
     => m1_subset_1(k5_lattices(A),u1_struct_0(A)) ) ),
    file(lattices,k5_lattices),
    []).

fof(dt_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    []).

fof(dt_k5_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)) ) ),
    file(relset_1,k5_relset_1),
    []).

fof(dt_k5_setwiseo,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k5_finsub_1(A))
        & m1_subset_1(C,k5_finsub_1(A)) )
     => m1_subset_1(k5_setwiseo(A,B,C),k5_finsub_1(A)) ) ),
    file(setwiseo,k5_setwiseo),
    []).

fof(dt_k5_substlat,axiom,(
    ! [A,B] : 
      ( v3_lattices(k5_substlat(A,B))
      & l3_lattices(k5_substlat(A,B)) ) ),
    file(substlat,k5_substlat),
    []).

fof(dt_k7_funct_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => ( v1_funct_1(k7_funct_2(A,B,C,D,E))
        & v1_funct_2(k7_funct_2(A,B,C,D,E),A,C)
        & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) ) ) ),
    file(funct_2,k7_funct_2),
    []).

fof(dt_k7_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k7_relat_1(A,B)) ) ),
    file(relat_1,k7_relat_1),
    []).

fof(dt_k7_setwiseo,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(B,B),B)
        & m1_relset_1(C,k2_zfmisc_1(B,B),B)
        & m1_subset_1(D,k5_finsub_1(A))
        & v1_funct_1(E)
        & v1_funct_2(E,A,B)
        & m1_relset_1(E,A,B) )
     => m1_subset_1(k7_setwiseo(A,B,C,D,E),B) ) ),
    file(setwiseo,k7_setwiseo),
    []).

fof(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(dt_k8_heyting2,axiom,(
    ! [A,B] : 
      ( v1_finset_1(B)
     => ( v1_funct_1(k8_heyting2(A,B))
        & v1_funct_2(k8_heyting2(A,B),k4_partfun1(A,B),u1_struct_0(k5_substlat(A,B)))
        & m2_relset_1(k8_heyting2(A,B),k4_partfun1(A,B),u1_struct_0(k5_substlat(A,B))) ) ) ),
    file(heyting2,k8_heyting2),
    []).

fof(dt_l1_lattices,axiom,(
    ! [A] : 
      ( l1_lattices(A)
     => l1_struct_0(A) ) ),
    file(lattices,l1_lattices),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_l2_lattices,axiom,(
    ! [A] : 
      ( l2_lattices(A)
     => l1_struct_0(A) ) ),
    file(lattices,l2_lattices),
    []).

fof(dt_l3_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( l1_lattices(A)
        & l2_lattices(A) ) ) ),
    file(lattices,l3_lattices),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(dt_u1_lattices,axiom,(
    ! [A] : 
      ( l1_lattices(A)
     => ( v1_funct_1(u1_lattices(A))
        & v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(lattices,u1_lattices),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(dt_u2_lattices,axiom,(
    ! [A] : 
      ( l2_lattices(A)
     => ( v1_funct_1(u2_lattices(A))
        & v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(lattices,u2_lattices),
    []).

fof(existence_l1_lattices,axiom,(
    ? [A] : l1_lattices(A) ),
    file(lattices,l1_lattices),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_l2_lattices,axiom,(
    ? [A] : l2_lattices(A) ),
    file(lattices,l2_lattices),
    []).

fof(existence_l3_lattices,axiom,(
    ? [A] : l3_lattices(A) ),
    file(lattices,l3_lattices),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(fc11_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k2_relat_1(A)) ) ),
    file(finseq_1,fc11_finseq_1),
    []).

fof(fc17_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(finseq_1,fc17_finseq_1),
    []).

fof(fc1_finsub_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_zfmisc_1(A))
      & v1_finsub_1(k1_zfmisc_1(A))
      & v3_finsub_1(k1_zfmisc_1(A))
      & v4_finsub_1(k1_zfmisc_1(A)) ) ),
    file(finsub_1,fc1_finsub_1),
    []).

fof(fc1_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_1),
    []).

fof(fc1_rfinseq,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(B) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_funct_1(k7_relat_1(A,B))
        & v1_finset_1(k7_relat_1(A,B)) ) ) ),
    file(rfinseq,fc1_rfinseq),
    []).

fof(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

fof(fc1_substlat,axiom,(
    ! [A,B] : ~ v1_xboole_0(k1_substlat(A,B)) ),
    file(substlat,fc1_substlat),
    []).

fof(fc1_wellfnd1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k4_partfun1(A,B))
      & v1_fraenkel(k4_partfun1(A,B)) ) ),
    file(wellfnd1,fc1_wellfnd1),
    []).

fof(fc2_finseq_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    []).

fof(fc2_finsub_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k5_finsub_1(A))
      & v1_finsub_1(k5_finsub_1(A))
      & v3_finsub_1(k5_finsub_1(A))
      & v4_finsub_1(k5_finsub_1(A)) ) ),
    file(finsub_1,fc2_finsub_1),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc2_substlat,axiom,(
    ! [A,B] : 
      ( ~ v3_struct_0(k5_substlat(A,B))
      & v3_lattices(k5_substlat(A,B)) ) ),
    file(substlat,fc2_substlat),
    []).

fof(fc3_substlat,axiom,(
    ! [A,B] : 
      ( ~ v3_struct_0(k5_substlat(A,B))
      & v3_lattices(k5_substlat(A,B))
      & v4_lattices(k5_substlat(A,B))
      & v5_lattices(k5_substlat(A,B))
      & v6_lattices(k5_substlat(A,B))
      & v7_lattices(k5_substlat(A,B))
      & v8_lattices(k5_substlat(A,B))
      & v9_lattices(k5_substlat(A,B))
      & v10_lattices(k5_substlat(A,B)) ) ),
    file(substlat,fc3_substlat),
    []).

fof(fc4_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_funct_1(k7_relat_1(A,B)) ) ) ),
    file(funct_1,fc4_funct_1),
    []).

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(fc4_substlat,axiom,(
    ! [A,B] : 
      ( ~ v3_struct_0(k5_substlat(A,B))
      & v3_lattices(k5_substlat(A,B))
      & v4_lattices(k5_substlat(A,B))
      & v5_lattices(k5_substlat(A,B))
      & v6_lattices(k5_substlat(A,B))
      & v7_lattices(k5_substlat(A,B))
      & v8_lattices(k5_substlat(A,B))
      & v9_lattices(k5_substlat(A,B))
      & v10_lattices(k5_substlat(A,B))
      & v11_lattices(k5_substlat(A,B))
      & v12_lattices(k5_substlat(A,B))
      & v13_lattices(k5_substlat(A,B))
      & v14_lattices(k5_substlat(A,B))
      & v15_lattices(k5_substlat(A,B)) ) ),
    file(substlat,fc4_substlat),
    []).

fof(fraenkel_a_2_0_substlat,axiom,(
    ! [A,B,C] : 
      ( r2_hidden(A,a_2_0_substlat(B,C))
    <=> ? [D] : 
          ( m1_subset_1(D,k5_finsub_1(k4_partfun1(B,C)))
          & A = D
          & ! [E] : 
              ( r2_hidden(E,D)
             => v1_finset_1(E) )
          & ! [E] : 
              ( m1_subset_1(E,k4_partfun1(B,C))
             => ! [F] : 
                  ( m1_subset_1(F,k4_partfun1(B,C))
                 => ( ( r2_hidden(E,D)
                      & r2_hidden(F,D)
                      & r1_tarski(E,F) )
                   => E = F ) ) ) ) ) ),
    file(substlat,a_2_0_substlat),
    []).

fof(fraenkel_a_2_1_heyting2,axiom,(
    ! [A,B,C] : 
      ( v1_finset_1(C)
     => ( r2_hidden(A,a_2_1_heyting2(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,k5_finsub_1(k4_partfun1(B,C)))
            & A = D
            & ! [E] : 
                ( r2_hidden(E,D)
               => v1_finset_1(E) )
            & ! [E] : 
                ( m1_subset_1(E,k4_partfun1(B,C))
               => ! [F] : 
                    ( m1_subset_1(F,k4_partfun1(B,C))
                   => ( ( r2_hidden(E,D)
                        & r2_hidden(F,D)
                        & r1_tarski(E,F) )
                     => E = F ) ) ) ) ) ) ),
    file(heyting2,a_2_1_heyting2),
    []).

fof(free_g3_lattices,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A) )
     => ! [D,E,F] : 
          ( g3_lattices(A,B,C) = g3_lattices(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) ),
    file(lattices,g3_lattices),
    []).

fof(idempotence_k1_finsub_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k1_finsub_1(A,B,B) = B ) ),
    file(finsub_1,k1_finsub_1),
    []).

fof(idempotence_k2_substlat,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(C,k1_substlat(A,B))
        & m1_subset_1(D,k1_substlat(A,B)) )
     => k2_substlat(A,B,C,C) = C ) ),
    file(substlat,k2_substlat),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(idempotence_k5_setwiseo,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k5_finsub_1(A))
        & m1_subset_1(C,k5_finsub_1(A)) )
     => k5_setwiseo(A,B,B) = B ) ),
    file(setwiseo,k5_setwiseo),
    []).

fof(l37_heyting2,axiom,(
    ! [A,B] : 
      ( v1_finset_1(B)
     => ! [C] : 
          ( m1_subset_1(C,k4_partfun1(A,B))
         => ( v1_finset_1(C)
           => k8_funct_2(k4_partfun1(A,B),u1_struct_0(k5_substlat(A,B)),k8_heyting2(A,B),C) = k2_setwiseo(k4_partfun1(A,B),C) ) ) ) ),
    file(heyting2,l37_heyting2),
    []).

fof(rc1_finseq_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    []).

fof(rc1_fraenkel,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A) ) ),
    file(fraenkel,rc1_fraenkel),
    []).

fof(rc1_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

fof(rc1_heyting2,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_fraenkel(A) ) ),
    file(heyting2,rc1_heyting2),
    []).

fof(rc1_setwiseo,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k5_finsub_1(A))
      & v1_xboole_0(B)
      & v1_finset_1(B) ) ),
    file(setwiseo,rc1_setwiseo),
    []).

fof(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

fof(rc1_substlat,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_subset_1(C,k1_substlat(A,B))
      & ~ v1_xboole_0(C) ) ),
    file(substlat,rc1_substlat),
    []).

fof(rc2_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    []).

fof(rc2_setwiseo,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k5_finsub_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(setwiseo,rc2_setwiseo),
    []).

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc2_substlat,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_subset_1(C,k4_partfun1(A,B))
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_finset_1(C) ) ),
    file(substlat,rc2_substlat),
    []).

fof(rc3_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    []).

fof(rc3_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    []).

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(rc4_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    []).

fof(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

fof(rc6_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    []).

fof(rc7_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    []).

fof(rc8_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    []).

fof(redefinition_k1_finsub_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k1_finsub_1(A,B,C) = k2_xboole_0(B,C) ) ),
    file(finsub_1,k1_finsub_1),
    []).

fof(redefinition_k1_partfun1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( v1_funct_1(E)
        & m1_relset_1(E,A,B)
        & v1_funct_1(F)
        & m1_relset_1(F,C,D) )
     => k1_partfun1(A,B,C,D,E,F) = k5_relat_1(E,F) ) ),
    file(partfun1,k1_partfun1),
    []).

fof(redefinition_k2_binop_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_subset_1(E,A)
        & m1_subset_1(F,B) )
     => k2_binop_1(A,B,C,D,E,F) = k1_binop_1(D,E,F) ) ),
    file(binop_1,k2_binop_1),
    []).

fof(redefinition_k2_partfun1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => k2_partfun1(A,B,C,D) = k7_relat_1(C,D) ) ),
    file(partfun1,k2_partfun1),
    []).

fof(redefinition_k2_setwiseo,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k2_setwiseo(A,B) = k1_tarski(B) ) ),
    file(setwiseo,k2_setwiseo),
    []).

fof(redefinition_k2_substlat,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(C,k1_substlat(A,B))
        & m1_subset_1(D,k1_substlat(A,B)) )
     => k2_substlat(A,B,C,D) = k2_xboole_0(C,D) ) ),
    file(substlat,k2_substlat),
    []).

fof(redefinition_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k4_relset_1(A,B,C) = k1_relat_1(C) ) ),
    file(relset_1,k4_relset_1),
    []).

fof(redefinition_k5_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k5_relset_1(A,B,C) = k2_relat_1(C) ) ),
    file(relset_1,k5_relset_1),
    []).

fof(redefinition_k5_setwiseo,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k5_finsub_1(A))
        & m1_subset_1(C,k5_finsub_1(A)) )
     => k5_setwiseo(A,B,C) = k2_xboole_0(B,C) ) ),
    file(setwiseo,k5_setwiseo),
    []).

fof(redefinition_k7_funct_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E) ) ),
    file(funct_2,k7_funct_2),
    []).

fof(redefinition_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(redefinition_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(redefinition_r1_heyting1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_finsub_1(A))
        & m1_subset_1(C,k5_finsub_1(A)) )
     => ( r1_heyting1(A,B,C)
      <=> r1_tarski(B,C) ) ) ),
    file(heyting1,r1_heyting1),
    []).

fof(reflexivity_r1_heyting1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_finsub_1(A))
        & m1_subset_1(C,k5_finsub_1(A)) )
     => r1_heyting1(A,B,B) ) ),
    file(heyting1,r1_heyting1),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(s4_funct_2__e5_37__heyting2,axiom,(
    ! [A,B] : 
      ( v1_finset_1(B)
     => ? [C] : 
          ( v1_funct_1(C)
          & v1_funct_2(C,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B))
          & m2_relset_1(C,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B))
          & ! [D] : 
              ( m1_subset_1(D,k5_finsub_1(k4_partfun1(A,B)))
             => k8_funct_2(k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B),C,D) = k3_substlat(A,B,D) ) ) ) ),
    file(heyting2,s4_funct_2__e5_37__heyting2),
    []).

fof(t11_substlat,axiom,(
    ! [A,B,C] : 
      ( m2_subset_1(C,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B))
     => k3_substlat(A,B,C) = C ) ),
    file(substlat,t11_substlat),
    []).

fof(t13_substlat,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B)))
     => ! [D] : 
          ( m1_subset_1(D,k5_finsub_1(k4_partfun1(A,B)))
         => k3_substlat(A,B,k1_finsub_1(k5_finsub_1(k4_partfun1(A,B)),k3_substlat(A,B,C),D)) = k3_substlat(A,B,k1_finsub_1(k5_finsub_1(k4_partfun1(A,B)),C,D)) ) ) ),
    file(substlat,t13_substlat),
    []).

fof(t14_setwiseo,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k5_finsub_1(A))
         => ! [C] : 
              ( r2_hidden(C,B)
             => m1_subset_1(C,A) ) ) ) ),
    file(setwiseo,t14_setwiseo),
    []).

fof(t19_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] : 
          ( ( v1_funct_1(E)
            & v1_funct_2(E,B,C)
            & m2_relset_1(E,B,C) )
         => ( ~ ( B = k1_xboole_0
                & C != k1_xboole_0
                & A != k1_xboole_0 )
           => ( v1_funct_1(k1_partfun1(A,B,B,C,D,E))
              & v1_funct_2(k1_partfun1(A,B,B,C,D,E),A,C)
              & m2_relset_1(k1_partfun1(A,B,B,C,D,E),A,C) ) ) ) ) ),
    file(funct_2,t19_funct_2),
    []).

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t21_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] : 
          ( ( v1_relat_1(E)
            & v1_funct_1(E) )
         => ( r2_hidden(C,A)
           => ( B = k1_xboole_0
              | k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) ) ) ) ) ),
    file(funct_2,t21_funct_2),
    []).

fof(t26_lattice2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => v3_binop_1(u2_lattices(A),u1_struct_0(A)) ) ),
    file(lattice2,t26_lattice2),
    []).

fof(t26_substlat,axiom,(
    ! [A,B] : k5_lattices(k5_substlat(A,B)) = k1_xboole_0 ),
    file(substlat,t26_substlat),
    []).

fof(t27_lattice2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & l2_lattices(A) )
     => v1_binop_1(u2_lattices(A),u1_struct_0(A)) ) ),
    file(lattice2,t27_lattice2),
    []).

fof(t28_lattice2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( v1_setwiseo(u2_lattices(A),u1_struct_0(A))
       => k5_lattices(A) = k3_binop_1(u1_struct_0(A),u2_lattices(A)) ) ) ),
    file(lattice2,t28_lattice2),
    []).

fof(t29_lattice2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v5_lattices(A)
        & l2_lattices(A) )
     => v2_binop_1(u2_lattices(A),u1_struct_0(A)) ) ),
    file(lattice2,t29_lattice2),
    []).

fof(t2_heyting2,axiom,(
    ! [A,B,C,D] : 
      ( ( r2_hidden(D,k1_substlat(A,B))
        & r2_hidden(C,D) )
     => ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finset_1(C) ) ) ),
    file(heyting2,t2_heyting2),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

fof(t2_tarski,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t46_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(k2_relat_1(A),k1_relat_1(B))
           => k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A) ) ) ) ),
    file(relat_1,t46_relat_1),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t65_setwiseo,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C,D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,k2_zfmisc_1(B,B),B)
                & m2_relset_1(D,k2_zfmisc_1(B,B),B) )
             => ( ( v1_binop_1(D,B)
                  & v2_binop_1(D,B)
                  & v3_binop_1(D,B)
                  & v1_setwiseo(D,B) )
               => ! [E] : 
                    ( ( v1_funct_1(E)
                      & v1_funct_2(E,A,k5_finsub_1(C))
                      & m2_relset_1(E,A,k5_finsub_1(C)) )
                   => ! [F] : 
                        ( ( v1_funct_1(F)
                          & v1_funct_2(F,k5_finsub_1(C),B)
                          & m2_relset_1(F,k5_finsub_1(C),B) )
                       => ( ( k8_funct_2(k5_finsub_1(C),B,F,k1_setwiseo(C)) = k3_binop_1(B,D)
                            & ! [G] : 
                                ( m1_subset_1(G,k5_finsub_1(C))
                               => ! [H] : 
                                    ( m1_subset_1(H,k5_finsub_1(C))
                                   => k8_funct_2(k5_finsub_1(C),B,F,k5_setwiseo(C,G,H)) = k2_binop_1(B,B,B,D,k8_funct_2(k5_finsub_1(C),B,F,G),k8_funct_2(k5_finsub_1(C),B,F,H)) ) ) )
                         => ! [G] : 
                              ( m1_subset_1(G,k5_finsub_1(A))
                             => k8_funct_2(k5_finsub_1(C),B,F,k10_setwiseo(A,C,G,E)) = k7_setwiseo(A,B,D,G,k7_funct_2(A,k5_finsub_1(C),B,E,F)) ) ) ) ) ) ) ) ) ),
    file(setwiseo,t65_setwiseo),
    []).

fof(t67_lattice2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => v1_setwiseo(u2_lattices(A),u1_struct_0(A)) ) ),
    file(lattice2,t67_lattice2),
    []).

fof(t67_setwiseo,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k5_finsub_1(A))
            & m2_relset_1(B,A,k5_finsub_1(A)) )
         => ( B = k11_setwiseo(A)
          <=> ! [C] : 
                ( m1_subset_1(C,A)
               => k8_funct_2(A,k5_finsub_1(A),B,C) = k2_setwiseo(A,C) ) ) ) ) ),
    file(setwiseo,t67_setwiseo),
    []).

fof(t68_setwiseo,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B,C] : 
          ( m1_subset_1(C,A)
         => ( r2_hidden(B,k8_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),C))
          <=> B = C ) ) ) ),
    file(setwiseo,t68_setwiseo),
    []).

fof(t69_lattice2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k5_finsub_1(A))
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v10_lattices(C)
                & v13_lattices(C)
                & l3_lattices(C) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,u1_struct_0(C))
                    & m2_relset_1(D,A,u1_struct_0(C)) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,u1_struct_0(C))
                        & m2_relset_1(E,A,u1_struct_0(C)) )
                     => ( k2_partfun1(A,u1_struct_0(C),D,B) = k2_partfun1(A,u1_struct_0(C),E,B)
                       => k2_lattice2(A,C,B,D) = k2_lattice2(A,C,B,E) ) ) ) ) ) ) ),
    file(lattice2,t69_lattice2),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t6_heyting2,axiom,(
    ! [A,B,C] : 
      ( ( v1_finset_1(C)
        & m1_subset_1(C,k4_partfun1(A,B)) )
     => r2_hidden(k2_setwiseo(k4_partfun1(A,B),C),k1_substlat(A,B)) ) ),
    file(heyting2,t6_heyting2),
    []).

fof(t70_setwiseo,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B,C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k5_finsub_1(B))
            & m2_relset_1(C,A,k5_finsub_1(B)) )
         => ! [D] : 
              ( m1_subset_1(D,k5_finsub_1(A))
             => ! [E] : 
                  ( r2_hidden(E,k10_setwiseo(A,B,D,C))
                <=> ? [F] : 
                      ( m1_subset_1(F,A)
                      & r2_hidden(F,D)
                      & r2_hidden(E,k8_funct_2(A,k5_finsub_1(B),C,F)) ) ) ) ) ) ),
    file(setwiseo,t70_setwiseo),
    []).

fof(t72_funct_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(B,A)
       => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ),
    file(funct_1,t72_funct_1),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t7_substlat,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B)))
     => ! [D] : 
          ( v1_finset_1(D)
         => ( ( r2_hidden(D,C)
              & ! [E] : 
                  ( v1_finset_1(E)
                 => ( ( r2_hidden(E,C)
                      & r1_tarski(E,D) )
                   => E = D ) ) )
           => r2_hidden(D,k3_substlat(A,B,C)) ) ) ) ),
    file(substlat,t7_substlat),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).

fof(t8_substlat,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B)))
     => r1_tarski(k3_substlat(A,B,C),C) ) ),
    file(substlat,t8_substlat),
    []).

fof(t91_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(A,k1_relat_1(B))
       => k1_relat_1(k7_relat_1(B,A)) = A ) ) ),
    file(relat_1,t91_relat_1),
    []).

fof(t9_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    []).

fof(t9_substlat,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B)))
     => ( C = k1_xboole_0
       => k3_substlat(A,B,C) = k1_xboole_0 ) ) ),
    file(substlat,t9_substlat),
    []).